# How do you write x³+7x²+10x in factored form?

May 1, 2018

$x \left(x + 2\right) \left(x + 5\right)$

#### Explanation:

First, we can factor out $x$, because all of the terms of the polynomial include $x$:
$= x \left({x}^{2} + 7 x + 10\right)$ Now, looking at $\left({x}^{2} + 7 x + 10\right)$:
Since the ${x}^{2}$ term's coefficient is one, we know the factoring will look something like:
$\left(x \pm a\right) \left(x \pm b\right)$. Looking at the other terms of the polynomial, we see that factors of $10$ will have to add up to $7$ (both are positive so both signs will be positive. Factors of 10:
$\left(1 , 10\right)$
$\left(2 , 5\right)$
And after this, it's the same in the opposite order. We can see that $2 + 5 = 7$, so $2$ and $5$ must go in to the equation:
$\left(x + 2\right) \left(x + 5\right)$. Inputting this into the other we get:
$x \left(x + 2\right) \left(x + 5\right)$